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Re: RMP 66, its initial calculation and diplation proof
Posted:
May 7, 2009 11:45 AM


Dear Forum members,
Condensing my overly long discussion, let me begin again by mentioning that Chace, 1927, did not report the following transliterated data. The data was provided by Franz when discussing RMP 66.
C'est la quantitée journalière à faire selon qui advient 1  365 2  730 4  1460 "3  243 '3 '10  36 '2 '2190  '6 Total 8 "3 '10 '2190
Chace added [ 8 2920 ] a line following line 4  2920
That is, to fairly parse the meaning of Ahmes' transliterated information, Chace's footnotes need not be read in excessive detail, such as  skip the RMP 23 discussion.
It is easy to fully translate Ahmes (if that was his name) and RMP 66's problem statement, initial calculation, and proof by considering:
1. statement of the problem: convert 10 hekat to ro and divide by 365 days, to obtain the daily usage:
3200/365
a. intermediate answer: 8 + 280/365
b. final answer : 8 + 2/3 + 1/10 + 1/2190
2. Proof:
a. by taking the first column
1  365 2  730 4  1460 [8  2920]
shows that 8 x 365 = 2920, the quotient 8's proof,
b. the remainder (3200  2920) = 280/365
was proven by:
(1) 365 times 2/3 = 243 1/3
(2) 365 times 1/10 = 36 1/2
(3) adding 243 1/3 + 36 1/2 = 279 5/6
(4) The missing 1/6 was found by
(5) 2190 times 1/365 = 6, or 1/6 times 365 = 2190
or,
(6). (243 1/3 + 36 1/2 + 1/6) = 280/365
Thus, Ahmes proved that
8 + 2/3 + 1/10 + 1/2190
was initially calculated by the quotient and remainder:
8 + 280/365
Q.E.D.



